@TedShifrin Okay, so I just started working $u_t + \frac{1}{2}u_{xx} = x + t,\ u(0,\ t) = u(5,\ t) = u(x,\ 0) = 0$. Applying Duhamel's principle, I'm solving $u_s + \frac{1}{2}u_{xx} = 0,\ u(0,\ s) = u(5,\ s) = 0$, which I get to be $u = \sum_{n = 1}^\infty B_n e^{-\frac{n^2 \pi^2 s}{50}}\sin(\frac{n\pi x}{5})$.

When I apply the IC $u(x,\ s) = x + s$, I get $x + s = \sum_{n = 1}^\infty B_n e^{-\frac{n^2 \pi^2 s}{50}}\sin(\frac{n\pi x}{5})$, but I am not allowed to assume $s = 0$, so I cannot eliminate the exponential factor and solve the Fourier series?

@AMDG first one is a bit subtle

So complex differentiable functions are called "holomorphic" and ones that are holomorphic except for their poles are called "meromorphic". Is there a word for functions that are holomorphic except for branch cuts?

@AMDG nice one

i laughed

@geocalc33 hey mon!

Oop, someone dropped an r-bomb (see above :P)

@PenAndPaperMathematics hello

Did you move yet?

:>

@geocalc33 what r you studying on?

yeah

@PenAndPaperMathematics What do you mean?

Math-wise?

Self-study ?

I actually got some work as well, but might not be long-term

the toilet

Just trying to understand a function that's a sum of meromorphic functions

Nice whoosh over my head

@geocalc33 finite sum?

reference to an earlier youtube reference

@robjohn infinite, but I could study a truncated version

I'm going to study some commutative algebra. It's tough to finish any book these days, they make them around 400 pages...

reminds me of a saying i will attribute to joyce, i am sorry i wrote you such a long letter, but i did not have time to write a short one.

Wish I had some NZT-48

like in Limitless, but with no side effects

I'm doing exercises from topology

I'm off tobacco officially guys...

@Jakobian nice!

Topology is the gateway drug to higher math

i use tea

analysis is real math

The annals of math is like porn for mathematicians

the first 3 terms are $\Gamma(1+1/z)-1/2+\zeta(-z)$

It's a renowned journal which they shouldn't have named that... :o

@geocalc33 how can we get the rest of the terms ?

so many possibilities with that one...

bit of a black hole, really

@geocalc33 it's nice to see that you're working in number theory now, but don't let the primes get the best of you :)

the rest are just $-(1/2!)\zeta(-2z)+(1/3!)\zeta(-3z)-(1/4!)\zeta(-4z)...$

Does this series have a name to google?

@geocalc33 what property of this series are you interested in?

no

@BGreen These are not even functions. Meromorphic functions are still functions mapping to $\Bbb C\cup\{\infty\}$.

@copper.hat yeah, I think analysis goes deeper than algebra. Algebra is more organizational / categorical

@PenAndPaperMathematics it was a silly joke, meant to provoke

But each theory is vital to have explored

@PenAndPaperMathematics interested in whether $\Re(z)=1$ is a natural boundary, complex roots

@PenAndPaperMathematics i can scrape along with analysis, but algebra leaves me paralysed

@copper.hat don't disrespect algebraic structures, pls :)

you mean the abstract nonsense?

Algebra came before analysis

Yoo, the professor said they'll write the letter. I'm kind of shocked because the app is due on Monday ;-;'

@PenAndPaperMathematics how do you know?

@geocalc33 I will change my course today to $\Bbb{C}$ analysis. I will try to get to where you are, but that will take some time.

Analytic continuation stuff it sounds like. I own a hardcopy of "Visual Complex Analysis".

Hey, I'm taking complex analysis next semester. I don't mean to bud in, but is this grad or undergrad level?

I also need this background, but haven't gotten around to it yet.

Both probably, sounds like he's researching something, but Analytic continuation is indeed tought to undergrads at the finer schools

Ooh, ok

Analytic continuation is not seriously in undergraduate complex analysis courses.

I didn't know.

:D

I say this having taught for 40+ years, including both undergrad and grad complex anslysis.

Lots of people talk a lot here without knowing, but pretending they do.

I know right

What level is "Visual Complex Analysis"?

It's apparently both

but it's not as formally presented as most Springer books

Sounds like optometry to me.

I understood that joke.

Undergrad, I think, but quite non-standard. I do not know the book.

Maybe it can be something I peruse in the summer before I take the course.

I'll be taking that and abstract algebra. Not sure what else yet.

Two serious math courses is enough math for most students.

Hm, alright. I'll have to look at some electives then.

@copper Any word from missing @leslie?

Missing? :C

@TedShifrin Have not seen for a few days.

I have an email. Perhaps I should use it.

If I have $f:[0, 1]\to\mathbb{R}$ with $\text{diam}\ f^{-1}(x) < \delta$, can I prove there exist $\varepsilon > 0$ such that if $|f-g|<\varepsilon$ then $\text{diam}\ g^{-1}(x) < \delta$?

I’d prefer $y$ to $x$ to keep track of domain/codomain. Is this a fixed $x$?

it can be assumed to be for all $x\in \mathbb{R}$, but fixed works too

I’m switching to $y$.

that's odd

Draw a function that’s $0$ on a closed interval of whatever length. A function $\epsilon$ close can be $0$ on a longer interval.

@TedShifrin Your call, I am not on email terms.

Sent.

Hopefully all is well.

@TedShifrin he hasn't been on the site since yesterday around noon (not using mod powers).

@TedShifrin I hope all is well.

I said we all so hoped.